Where do you live and what kind of grass do you have? The fertilizer applications depend on that. The lime they are recommending is ordinary lime. Use dolomitic lime so you will get some magnesium.(you are slightly low). Your pH is okay as is, the lime is just to get it closer to the sweet spot. So there is no rush. I think I would put it off until late fall and do it then.

Thanks. I'm in southwestern CT with a mix of fescue/rye/bluegrass.

Fescue needs 2-3 lb/k of nitrogen a year, KBG and rye 3-4 lb/k. If you leave the grass clippings on the lawn, you can reduce fertilizer by 25%. If you use synthetic fertilizer, I think I'd do a slow release fertilizer in early fall (late August/early September) and a fast release in late fall after the grass has stopped growing but before the ground freezes. Do a slow release in late spring around Memorial Day. If you use organic fertilizer, do an application in mid to late August and mid to late May. The late fall application needs to be synthetic fast release. Aim to put down 1 lb/k of nitrogen for each application. If you decide to do just two applications, like they suggest, do them early fall and late fall.